N.29 Cleb­sch-Gor­dan ta­bles are bidi­rec­tional

The fact that you can read the ta­bles ei­ther by rows or by columns is
due to the or­tho­nor­mal­ity of the states in­volved. In terms of the
real vec­tors of physics, it is sim­ply an ex­pres­sion of the fact that
the com­po­nent of one unit vec­tor in the di­rec­tion of an­other unit
vec­tor is the same as the com­po­nent of the sec­ond unit vec­tor in the
di­rec­tion of the first.